hw5_sol

hw5_sol - 10-60.a) n -1 = 1 - 0.99 = 0.01 2 /2, n-1 = 31.32...

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10-60.a) ( 29 ( 29 [ ] 2 2 2 2 2 /2 ,1 2 1 22 2 , 1 1 2 3297 786421 15 4410.03 1 14 1 0.9 9 0.01 31.32 4.07 ( 1 )( 1) , 1971.3,15169.6 i i n n nn x x n s n nsns a a aa a c c s cc s - -- - -- = == - = -= = =   
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 A B C D E F G H I J Ex. 11-50.a) data (x) freq (f) f*x f*x^2 LB UB Prob ei Chi_Sq 2.10 16 33.6 70.56 2.105 0.0097 8.30 7.15 2.11 28 59.08 124.6588 2.105 2.115 0.0255 21.74 1.80 2.12 41 86.92 184.2704 2.115 2.125 0.0648 55.25 3.67 2.13 74 157.62 335.7306 2.125 2.135 0.1254 106.96 10.16 2.14 149 318.86 682.3604 2.135 2.145 0.1850 157.78 0.49 2.15 256 550.4 1183.36 2.145 2.155 0.2079 177.33 34.90 2.16 137 295.92 639.1872 2.155 2.165 0.1780 151.86 1.45 2.17 82 177.94 386.1298 2.165 2.175 0.1162 99.09 2.95 2.18 40 87.2 190.096 2.175 2.185 0.0577 49.26 1.74 2.19 19 41.61 91.1259 2.185 2.195 0.0219 18.65 0.01 2.20 11 24.2 53.24 2.195 0.0080 6.79 2.62 Totals 853 1833.35 3940.719 66.94 mean 2.149297 "=D17/C17 std dev 0.018957 "=SQRT((E17-D17^2/C17)/(C17-1)) Prob "=NORMSDIST((G6-$C$19)/$C$20)-NORMSDIST((F6-$C$19)/$C$20) ei "=$C$17*H6 Chi_Sq "=(C6-I6)^2/I6 df is k-p-1=11-2-1=8 alpha=0.05 from Table III Chi_Sq=15.507 Since the observed Chi_Sq is larger than the table value (66.94>15.507), reject Ho. The data are not from a normal distribution.
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28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 A B C D E F G H I J Ex. 11-50.b) data freq cum freq f_hat normal score 2.10 16 16 0.0187 "=D32/854 -2.08 "=NORMSINV(E32) 2.11 28 44 0.0515 -1.63 2.12 41 85 0.0995 -1.28 2.13 74 159 0.1862 -0.89 2.14 149 308 0.3607 -0.36 2.15 256 564 0.6604 0.41 2.16 137 701 0.8208 0.92 2.17 82 783 0.9169 1.38 2.18 40 823 0.9637 1.80 2.19 19 842 0.9859 2.20 2.20 11 853 0.9988 3.04 The plotted points appear to be a straight line. The normal distribution is plausible.
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This note was uploaded on 04/02/2008 for the course ISE 225 taught by Professor Palmer during the Spring '08 term at USC.

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hw5_sol - 10-60.a) n -1 = 1 - 0.99 = 0.01 2 /2, n-1 = 31.32...

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